For an equilateral triangle of side a, the distance of the centroid from any side is r=23a.
Given side a=43 cm =43×10−2 m.
So, r=2343×10−2=2×10−2 m.
The magnetic field at the centroid due to one side of the triangle is B1=4πrμ0I(sinθ1+sinθ2).
For an equilateral triangle, θ1=θ2=60∘.
B1=2×10−210−7×2(sin60∘+sin60∘)=10−5×(23+23)=3×10−5 T.
The total magnetic field at the centroid due to all three sides is B=3B1=33×10−5 T.
Comparing with B=α×10−5 T, we get α=33.